Solve the Absolute Value Inequality for x |3x+7|-7=4x

$| 3 x + 7 | - 7 = 4 x$

Step 1

Add $7$ to both sides of the equation.

$| 3 x + 7 | = 4 x + 7$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$3 x + 7 = \pm (4 x + 7)$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$3 x + 7 = 4 x + 7$

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$3 x + 7 - 4 x = 7$

Subtract $4 x$ from $3 x$ .

$- x + 7 = 7$

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- x = 7 - 7$

Subtract $7$ from $7$ .

$- x = 0$

Divide each term in $- x = 0$ by $- 1$ and simplify.

Divide each term in $- x = 0$ by $- 1$ .

$\frac{- x}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{0}{- 1}$

Divide $x$ by $1$ .

$x = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x = 0$

Next, use the negative value of the $\pm$ to find the second solution.

$3 x + 7 = - (4 x + 7)$

Simplify $- (4 x + 7)$ .

Rewrite.

$3 x + 7 = 0 + 0 - (4 x + 7)$

Simplify by adding zeros.

$3 x + 7 = - (4 x + 7)$

Apply the distributive property.

$3 x + 7 = - (4 x) - 1 \cdot 7$

Multiply.

Multiply $4$ by $- 1$ .

$3 x + 7 = - 4 x - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$3 x + 7 = - 4 x - 7$

Move all terms containing $x$ to the left side of the equation.

Add $4 x$ to both sides of the equation.

$3 x + 7 + 4 x = - 7$

Add $3 x$ and $4 x$ .

$7 x + 7 = - 7$

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$7 x = - 7 - 7$

Subtract $7$ from $- 7$ .

$7 x = - 14$

Divide each term in $7 x = - 14$ by $7$ and simplify.

Divide each term in $7 x = - 14$ by $7$ .

$\frac{7 x}{7} = \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 14}{7}$

Divide $x$ by $1$ .

$x = \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$x = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 0, - 2$

Step 4

Exclude the solutions that do not make $| 3 x + 7 | - 7 = 4 x$ true.

$x = 0$

Solve the Absolute Value Inequality for x |3x+7|-7=4x

Related Questions

Support LCMGCF.com by disabling your adblocker.